Abstract
This paper studies an on-line scheduling in medical laboratory. The sample of a patient is regarded as a job waiting to be scheduled, and each analyzer as a machine that may analyze several samples simultaneously as a batch. The samples arrive over time, and the information of each sample is not released until the sample arrives. Each sample is given a weight in a known range to represent its importance or urgency. Thus the medical laboratory scheduling can be described as a parallel-batch on-line scheduling problem. The objective is to minimize the maximum weighted flow-time. For the unbounded batch capacity model, a best possible on-line algorithm is established for any given range of weights. Moreover, for the bounded batch capacity model, a best possible on-line algorithm is presented for the range of weights 1 to 2.
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References
Anderson EJ, Potts CN (2004) Online scheduling of a single machine to minimize total weighted completion time. Math Oper Res 29:686–697
Cao J, Yuan J, Li W, Bu H (2011) Online scheduling on batching machines to minimize the total weighted completion time of jobs with precedence constraints and identical processing times. Int J Syst Sci 42:51–55
Li W, Yuan J (2011) Online scheduling on unbounded parallel-batch machines to minimize maximum flow-time. Inf Process Lett 111:907–911
Li X, Rafaliya N, Baki MF, Chaouch BA (2017) Scheduling elective surgeries: the tradeoff among bed capacity, waiting patients and operating room utilization using goal programming. Health Care Manag Sci 20:33–54
Liu P, Lu X, Fang Y (2012) A best possible deterministic on-line algorithm for minimizing makespan on parallel batch machines. J Sched 15:77–81
Liu L, Tang G, Fan B, Wang X (2015) Two-person cooperative games on scheduling problems in outpatient pharmacy dispensing process. Spec Issue Comb Optim Health Care J Comb Optim 30:938–948
Miller HE, Pierskalla WP, Rath GJ (1976) Nurse scheduling using mathematical programming. Oper Res 24:857–870
Tian J, Cheng TCE, Ng CT, Yuan J (2009) Online scheduling on unbounded parallel-batch machines to minimize the makespan. Inf Process Lett 109:1211–1215
Warner DM (1976) Scheduling nursing personnel according to nursing preference: a mathematical programming approach. Oper Res 24:842–856
Zhang G, Cai X, Wong CK (2001) Online algorithms for minimizing makespan on batch processing machines. Naval Res Logist 48:241–258
Zhang G, Cai X, Wong CK (2003) Optimal on-line algorithms for scheduling on parallel batch processing machines. IIE Trans 35:175–181
Zhang X, Wang H, Wang X (2015) Patients scheduling problems with deferred deteriorated functions. Spec Issue Comb Optim Health Care J Comb Optim 30:1027–1041
Zhong L, Luo S, Wu L, Xu L, Yang J, Tang G (2014) A two-stage approach for surgery scheduling. J Comb Optim 27:545–556
Acknowledgements
This research was supported by the National Natural Science Foundation of China (Nos. 11571321, 11771406 and 11401065) and the Natural Science Foundation of Henan Province (No. 15IRTSTHN006).
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Li, W., Chai, X. The medical laboratory scheduling for weighted flow-time. J Comb Optim 37, 83–94 (2019). https://doi.org/10.1007/s10878-017-0211-4
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DOI: https://doi.org/10.1007/s10878-017-0211-4